He was educated in Turin and became a priest in 1851. After that, he soon rose to become domestic prelate of Pope Pius IX by 1857 and was internuncio in the Netherlands from 1863 to 1866. In May of that year he was elected titular archbishop of Tamiathis and served as papal nuncio to Belgium from then until 1868, when he was moved to Portugal. He remained as nuncio until his promotion to the cardinalate when he was returned to Rome.

On December 22, 1873, Oreglia was created a cardinal by Pius IX and two years later he became Prefect of the Sacred Congregation of Indulgences and Relics. He participated in the 1878 conclave that elected Pope Leo XIII and that pope elevated him to Camerlengo on March 27, 1882. Although Oreglia was forced to relinquish the post a year later, he became Camerlengo once more in 1885 and retained that post right up to his death twenty-eight years later. During this period he rose gradually to sub-Dean of the Sacred College by 1889 and to Dean by 1896.

When Leo XIII died in 1903, Cardinal Oreglia became the sole surviving cardinal elevated by Pope Pius IX. As therefore the only elector in the 1903 conclave with previous experience in electing a pope, and being the leader of the ultraconservative curial faction within the college who wanted a more intransigent pontiff than Leo was thought to have been, Oreglia is widely believed to have played a prominent role in the election of Giuseppe Sarto as Pius X. Indeed, some students of the papacy believe that without the guidance of Cardinal Oreglia, Cardinal Sarto would have chosen to refuse the papacy even when he had obtained 55 of the 60 available votes.

Nevertheless, Oreglia is also said to have vehemently protested against the announcement by Cardinal Jan Puzyna de Kosielsko regarding the civil veto of Emperor Franz Joseph of Austria against the name of Cardinal Mariano Rampolla, Leo's Secretary of State. Oreglia is also rumored to have prohibited the use of the method of election known as accessus in the 1903 Conclave[1] that elected Pope Pius X.

Oreglia retained his positions with the College of Cardinals right up to his death in 1913 at the age of eighty-five.